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Do Bees Build It Best? GeometryTrigonometry. BUILDING THE BEST.

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Presentation on theme: "Do Bees Build It Best? GeometryTrigonometry. BUILDING THE BEST."— Presentation transcript:

1 Do Bees Build It Best? GeometryTrigonometry

2 BUILDING THE BEST

3 NAILING DOWN AREA

4 HOW MANY CAN YOU FIND?

5 THATS ALL THERE IS!

6 HALVING YOUR WAY

7 PARALLELOGRAMS AND TRAPEZOIDS

8 FORMING FORMULAS

9 GOING INTO THE GALLERY

10 A RIGHT-TRIANGLE PAINTING

11 A TRIGONOMETRIC SUMMARY

12 MORE GALLERY MEASUREMENTS

13 A HOMEMADE TRIG TABLE

14 SHADOWS AND SAILBOATS

15 TRI-SQUARE RUG GAMES

16 ANY TWO SIDES WORK n LEG^2 + LEG^2 = HYP^2

17 IMPOSSIBLE RUGS

18 MAKE THE LINES COUNT

19 PROOF BY RUGS

20 THE POWER OF PYTHAGORAS

21 LESLIES FERTILE FLOWERS

22 FLOWERS FROM DIFFERENT SIDES

23 DONT FENCE ME IN

24 RECTANGLES ARE BORING!

25 MORE FENCING, BIGGER CORRALS

26 MORE OPINIONS ABOUT CORRALS

27 BUILDING THE BEST FENCE

28 FALLING BRIDGES

29 LESLIES FLORAL ANGLES

30 FLAT CUBES

31 FLAT BOXES

32 A VOLUMINOUS TASK

33 PUT YOUR FIST INTO IT

34 THE INS AND OUTS OF BOXES

35 A SCULPTURE GARDEN

36 THE WORLD OF PRISMS

37 SHEDDING LIGHT ON PRISMS

38 PYTHAGORAS AND THE BOX

39 BACK ON THE FARM

40 WHICH HOLDS MORE?

41 CEREAL BOX SIZES

42 A-TESSELLATING WE GO

43 A PORTFOLIO OF FORMULAS

44 THATS ALL THERE IS! n EACH TRIANGLE MUST HAVE AN AREA OF 2 UNITS n EACH TRIANGLE MUST HAVE ITS VERTICES ON PEGS n EACH TRIANGLE MUST HAVE A HORIZONTAL SIDE

45 HALVING YOUR WAY

46 FORMING FORMULAS n LOOK FOR WAYS TO CUT UP THE PARALLELOGRAMS AND TRAPEZOIDS INTO TRIANGLES

47 GOING INTO THE GALLERY n REMEMBER, THE HEIGHT IS ALSO THE ALTITUDE WHICH IS DRAWN PERPENDICULAR TO THE BASE

48 A RIGHT-TRIANGLE PAINTING n DRAW A RIGHT TRIANGLE THAT HAS A 55 DEGREE ANGLE n EXTEND BOTH SIDES SO THAT THEY ARE AT LEAST 10 CM IN LENGTH

49 A TRIGONOMETRIC SUMMARY n SIN A = OPPOSITE/HYPOTENUSE n COS A = ADJACENT/HYPOTENUSE n TAN A = OPPOSITE/ADJACENT

50 A HOMEMADE TRIG TABLE n DRAW A RIGHT TRIANGLE USING THE ASSIGNED ANGLE FOR YOUR GROUP n MEASURE ALL THE SIDES n COMPUTE THE RATIOS OF SIN, COS, AND TAN

51 MORE GALLERY MESUREMENTS n SIN A = OPPOSITE/HYPOTENUSE n COS A = ADJACENT/HYPOTENUSE n TAN A = OPPOSITE/ADJACENT

52 SHADOWS AND SAILBOATS

53 TRI-SQUARE RUG GAMES n AL WINS WHEN THE LARGEST OF THE 3 SQUARES HAS THE MOST AREA. n WHAT KIND OF TRIANGLE IS FORMED IN THIS SITUATION?

54 TRI-SQUARE RUG GAMES n BETTY WINS IF THE TWO SMALLER SQUARES HAVE MORE AREA THEN THE LARGEST n WHAT KIND OF TRIANGLE IS FORMED IN THIS SITUATION?

55 TRI-SQUARE RUG GAMES n IF THE TWO SMALLER SQUARES HAVE THE SAME AREA AS THE LARGEST, THIS IS A FAIR GAME. n WHAT KIND OF TRIANGLE IS FORMED IN THIS SITUATION?

56 ANY TWO SIDES WORK

57

58

59 IMPOSSIBLE RUGS n RULE: ANY TWO SIDES OF A TRIANGLE MUST BE GREATER THAN THE THIRD SIDE

60 MAKE THE LINES COUNT

61 THE POWER OF PYTHAGORAS

62

63 LESLIES FERTILE FLOWERS

64 FLOWERS FROM DIFFERENT SIDES

65 DONT FENCE ME IN n n RANCHER GONZALES CAN ONLY AFFORD 300 FEET OF FECNING n n MAKE AN INOUT TABLE OF VARIOUS LENGTHS AND WIDTHS

66 RECTANGLES ARE BORING! n RANCHER GONZALES NEPHEW JUAN HAS SUGGESTED RECTANGLES n AGAIN SHE MUST USE 300 FEET OF FENCING

67 MORE FENCING, BIGGER CORRALS n HOW DOES THE AREA OF A SQUARE CORRAL MADE 300 FT OF FENCING COMPARE TO 600 FT?

68 MORE FENCING, BIGGER CORRALS n HOW DOES THE AREA OF A AN EQUILATERAL TRIANGLE CORRAL MADE 300 FT OF FENCING COMPARE TO 600 FT?

69 MORE OPINIONS ABOUT CORRALS n ACES : PENTAGON n TWOS: HEXAGON n THREES: SEPTAGON n FOURS: OCTAGON n FIVES: 9 SIDED REG-POLY n SIXES: 10 SIDED REG-POLY

70 BUILDING THE BEST FENCE n AREA= (P^2/4n) * tan (90-180/n)

71 FALLING BRIDGES n USE OTHER APPROXIMATIONS FOR THE SQUARE ROOT OF 2

72 LESLIES FLORAL ANGLES n REMEMBER, THE INVERSE OF: ADDING?MULTIPLYING? SOMETHING SQUARED? n NOW WE NEED THE INVERSE OF OUR TRIG FUNCTIONS

73 FLAT BOXES n 132 CM SQUARED

74 FLAT BOXES n 108 CM SQUARED

75 A VOLUMINOUS TASK SURFACE AREAVOLUME n #1 n #2 n #3 n #4 n #5

76 A VOLUMINOUS TASK SURFACE AREAVOLUME n #7 n #8 n #9 n #10

77 PUT YOUR FIST INTO IT

78 THE INS AND OUTS OF BOXES

79 A SCULPTURE GARDEN n FIND A WAY TO ARRANGE 8 CUBES THAT USES THE LEAST AMOUNT OF PAINT

80 THE WORLD OF PRISMS n PRISM IS A SPECIAL TYPE OF SOLID GEOMETRIC FIGURE –THE INTIAL AND FINAL FACES ARE THE BASES –USUALLY 1 OR 2 BASES –PERPENDICULAR DISTANCE BETWEEN THE BASES IS THE HEIGHT

81 THE WORLD OF PRISMS n TRIANGULAR PRISMS n HEXAGONAL PRISMS n RECTANGULAR PRISMS

82 THE WORLD OF PRISMS n RIGHT PRISMS n OBLIQUE PRISMS

83 THE WORLD OF PRISMS n LATERAL FACES n LATERAL EDGES n BASES n LATERAL SURFACE AREA n TOTAL SURFACE AREA

84 PYTHAGORAS AND THE BOX

85 BACK ON THE FARM


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